A galvanometer has a resistance of `3663Omega`. A shunt `S` is connected across it such that (`1//34`) of the total current passes through the galvanometer. Then the value of the shunt is

Options

A. `3663 Omega`
B. `111 Omega`
C. `107.7 Omega`
D. `3555.3 Omega`

Explanation

To find the value of the shunt resistance \( S \) connected across the galvanometer, we can follow these steps:

### Step 1: Define the total current and current through the galvanometer
Let the total current be \( I \). According to the problem, \( \frac{1}{34} \) of the total current passes through the galvanometer. Therefore, the current through the galvanometer \( I_g \) can be expressed as:
\[ I_g = \frac{I}{34} \]

### Step 2: Calculate the current through the shunt
The current through the shunt \( I_s \) can be calculated by subtracting the current through the galvanometer from the total current:
\[ I_s = I - I_g = I - \frac{I}{34} = I \left(1 - \frac{1}{34}\right) = I \left(\frac{34 - 1}{34}\right) = I \left(\frac{33}{34}\right) \]

### Step 3: Write the voltage across the galvanometer
The voltage across the galvanometer \( V_{AB} \) can be expressed using Ohm's law:
\[ V_{AB} = I_g \cdot R_g = \left(\frac{I}{34}\right) \cdot R_g \]
where \( R_g = 3663 \, \Omega \) is the resistance of the galvanometer.

### Step 4: Write the voltage across the shunt
The voltage across the shunt \( V_{AB} \) can also be expressed as:
\[ V_{AB} = I_s \cdot S = \left(I \cdot \frac{33}{34}\right) \cdot S \]

### Step 5: Set the voltages equal
Since the galvanometer and the shunt are connected in parallel, the voltages across both must be equal:
\[ \left(\frac{I}{34}\right) \cdot R_g = \left(I \cdot \frac{33}{34}\right) \cdot S \]

### Step 6: Cancel \( I \) from both sides
Assuming \( I \neq 0 \), we can cancel \( I \) from both sides:
\[ \frac{R_g}{34} = \frac{33}{34} \cdot S \]

### Step 7: Solve for the shunt resistance \( S \)
Now, we can solve for \( S \):
\[ R_g = 33S \]
\[ S = \frac{R_g}{33} \]
Substituting the value of \( R_g \):
\[ S = \frac{3663}{33} \approx 111.0 \, \Omega \]

### Final Answer
Thus, the value of the shunt resistance \( S \) is approximately \( 111.0 \, \Omega \).

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